"Deadweight tonnage Deadweight tonnage (also known as deadweight; abbreviated to DWT, D.W.T., d.w.t., or dwt) or tons deadweight (TDW) is a measure of how much weight a ship can carry, not its weight, empty or in any degree of load. DWT is the sum of the weights of cargo, fuel, fresh water, ballast water, provisions, passengers, and crew. DWT is often used to specify a ship's maximum permissible deadweight (i.e. when she is fully loaded so that her Plimsoll line is at water level), although it may also denote the actual DWT of a ship not loaded to capacity. Deadweight"
"on ""W"" (also known as a tensor — not to be confused with a tensor field — of rank (0,""s""), where ""s"" is the number of factors of ""W"" in the product). Then the pullback Φ""F"" of ""F"" by Φ is a multilinear form on ""V"" defined by precomposing ""F"" with Φ. More precisely, given vectors ""v"",""v""...,""v"" in ""V"", Φ""F"" is defined by the formula which is a multilinear form on ""V"". Hence Φ is a (linear) operator from multilinear forms on ""W"" to multilinear forms on ""V"". As a special case, note that if ""F"" is a linear form"
"vector, F, denotes ""direction"" and ""strength"", whereas its corresponding scalar (""F"" ) denotes strength alone. Graphically, each vector is represented with an arrow that shows direction and a length that shows speed or strength. Vectors of consistent units (e.g. V in m/s or F in N) may be added and subtracted, graphically, by positioning tips and tails of the arrows, representing the input variables and drawing the resulting derived vector. Lift on a sail (L), acting as an airfoil, occurs in a direction perpendicular to the incident airstream (the apparent wind velocity, V, for the head sail) and is a"
"topological spaces, and motives. The operations are six functors. Usually these are functors between derived categories and so are actually left and right derived functors. The functors formula_2 and formula_1 form an adjoint functor pair, as do formula_3 and formula_4. Similarly, internal tensor product is left adjoint to internal Hom. Let be a morphism of schemes. The morphism ""f"" induces several functors. Specifically, it gives adjoint functors ""f"" and ""f"" between the categories of sheaves on ""X"" and ""Y"", and it gives the functor ""f"" of direct image with proper support. In the derived category, ""Rf"" admits a right adjoint"
"coordinates, ""u"" denotes the atomic displacement, and −""f"" and ""K"" are the first and second coefficients in the Taylor series. They are defined by and where the derivatives are evaluated at zero displacements. The negative sign is introduced in the definition of ""f"" for convenience. Thus ""f""(""L"") is a 3D vector that denotes the force at the atom L. Its three Cartesian components are denoted by f(L) where ""a"" = ""x"", ""y"", or ""z"". Similarly K(L,L’) is a 3x3 matrix, which is called the force- constant matrix between the atoms at L and L’. Its 9 elements are denoted by"
"middle finger mutually perpendicular to each other (at right angles), as shown in the diagram. The bolded letters in the directions above give a mnemonic way to remember the order. Another mnemonic for remembering the rule is the initialism ""FBI"", standing for Force (or otherwise motion), B the symbol for the magnetic field, and I the symbol for current. The subsequent letters correspond to subsequent fingers, counting from the top. Thumb -> F; First finger -> B; Second finger -> I There is also a Fleming's left hand rule (for electric motors). The appropriately handed rule can be recalled from"
"schematically using capital letters to stand for consonants in the root: Hence, the root F-M-L stands for all three-consonant roots, and F-S-T-L stands for all four-consonant roots. (Traditional Arabic grammar uses F-ʕ-L and F-ʕ-L-L, respectively, but the system used here appears in a number of grammars of spoken Arabic dialects and is probably less confusing for English speakers, since the forms are easier to pronounce than those involving ""ʕ"".) The following table lists the prefixes and suffixes to be added to mark tense, person, number and gender, and the stem form to which they are added. The forms involving a"
"""A"" with respect to the dual bases of ""W"" and ""V"", hence the name. Alternatively, as ""f"" is represented by ""A"" acting on the left on column vectors, ""f"" is represented by the same matrix acting on the right on row vectors. These points of view are related by the canonical inner product on R, which identifies the space of column vectors with the dual space of row vectors. Let ""S"" be a subset of ""V"". The annihilator of ""S"" in ""V"", denoted here ""S"", is the collection of linear functionals such that for all . That is, ""S"" consists"
"(−1)F In a quantum field theory with fermions, (−1) is a unitary, Hermitian, involutive operator where ""F"" is the fermion number operator. For the example of particles in the Standard Model, it is equal to the sum of the lepton number plus the baryon number, . The action of this operator is to multiply bosonic states by 1 and fermionic states by −1. This is always a global internal symmetry of any quantum field theory with fermions and corresponds to a rotation by 2π. This splits the Hilbert space into two superselection sectors. Bosonic operators commute with (−1) whereas fermionic"
"""f""(""x"", ""y"") where ""x"" and ""y"" are real numbers. So ""f"" is a function from the plane to the line. The space of all such smooth functions is acted upon by the group of diffeomorphisms of the plane and the diffeomorphisms of the line, i.e. diffeomorphic changes of coordinate in both the source and the target. This action splits the whole function space up into equivalence classes, i.e. orbits of the group action. One such family of equivalence classes is denoted by ""A"", where ""k"" is a non-negative integer. This notation was introduced by V. I. Arnold. A function ""f"""
"Point Prep School from 1983 to 1984 Forward observers in the U.S. military Forward observers in the U.S. military are artillery observers who carry the Military Occupational Specialty designator of ""13F"" in the United States Army and ""0861"" in the United States Marine Corps. They are officially called Joint Fire Support Specialists in the U.S. Army and Fire Support Men in the U.S. Marine Corps. They are colloquially known as FiSTers, regardless of whether they are members of a FiST (Fire Support Team). The Battalion Fire Support Officer (FSO) is the Officer in Charge of a Battalion Fire Support Element."
"VVO, or FDO (reboosts only), and SURGEON. In the back, right corner, behind the surgeon, the PAO (Public Affairs Officer) was occasionally present. The White FCR, which was used for Space Shuttle operations, was arranged in five rows. From left to right, as viewed from the rear of the room): The front row (the ""Trench"") had FDO (pronounced ""fido""), responsible for orbital guidance and orbital changes, depending on the phase of flight; either Guidance, a specialist in the procedures of those two high-energy, fast-paced phases of flight or rendezvous, a specialist in orbital rendezvous procedures; and GC, the controller responsible"
"the definition of F, F(""x"") is the state of the system at time ""t"" and consequently applying the definition once more, F(F(""x"")) is the state at time ""u"". But this is also F(""x""). In some contexts in mathematical physics, the mappings F are called propagation operators or simply propagators. In classical mechanics, the propagators are functions that operate on the phase space of a physical system. In quantum mechanics, the propagators are usually unitary operators on a Hilbert space. The propagators can be expressed as time-ordered exponentials of the integrated Hamiltonian. The asymptotic properties of time evolution are given by"
"Forward observers in the U.S. military Forward observers in the U.S. military are artillery observers who carry the Military Occupational Specialty designator of ""13F"" in the United States Army and ""0861"" in the United States Marine Corps. They are officially called Joint Fire Support Specialists in the U.S. Army and Fire Support Men in the U.S. Marine Corps. They are colloquially known as FiSTers, regardless of whether they are members of a FiST (Fire Support Team). The Battalion Fire Support Officer (FSO) is the Officer in Charge of a Battalion Fire Support Element. Forward Observers in the U.S. Army hold"
"so that ""F"" is a topological field. The Harrison topology is a topology on the set of orderings ""X"" of a formally real field ""F"". Each order can be regarded as a multiplicative group homomorphism from ""F"" onto ±1. Giving ±1 the discrete topology and ±1 the product topology induces the subspace topology on ""X"". The Harrison sets formula_11 form a subbasis for the Harrison topology. The product is a Boolean space (compact, Hausdorff and totally disconnected), and ""X"" is a closed subset, hence again Boolean. A fan on ""F"" is a preordering ""T"" with the property that if ""S"""
"formula_23 are done in three-dimensional space with the metric γ. This does not apply to operations of shifting indices in the space components of the four-tensors ""R"", ""T"". Thus ""T"" must be understood to be ""g""""T"" + ""g""""T"", which reduces to ""g""""T"" and differs in sign from γ""T"". The sum formula_25 is the logarithmic derivative of the determinant γ ≡ |γ| = − ""g"": Then for the complete set of Christoffel symbols formula_26 one obtains: where formula_27 are the three-dimensional Christoffel symbols constructed from γ: where the comma denotes partial derivative by the respective coordinate. With the Christoffel symbols ,"
"by and named by . Reynolds operators are used in fluid dynamics, functional analysis, and invariant theory, and the notation and definitions in these areas differ slightly. A Reynolds operator acting on φ is sometimes denoted by ""R""(""φ""), ""P""(""φ""), ""ρ""(""φ""),〈""φ""〉, or . Reynolds operators are usually linear operators acting on some algebra of functions, satisfying the identity and sometimes some other conditions, such as commuting with various group actions. In invariant theory a Reynolds operator ""R"" is usually a linear operator satisfying and Together these conditions imply that ""R"" is idempotent: ""R"" = ""R"". The Reynolds operator will also usually"
"and τ on ""E"" thus ""lift"" the formulas on F. Mumford also obtains an action simply transitive on the vertices of the building by passing to a subgroup of Γ = <ρ, σ, τ, −""I"">. The group Γ preserves the Q(α)-valued hermitian form on Q(ζ) and can be identified with ""U""(f) formula_15 ""GL""(""S"") where ""S"" = Z[α,½]. Since ""S""/(α) = F, there is a homomorphism of the group Γ into ""GL""(F). This action leaves invariant a 2-dimensional subspace in F and hence gives rise to a homomorphism Ψ of Γ into ""SL""(F), a group of order 16·3·7. On the other"
"Federal Flight Deck Officer Federal Flight Deck Officers (FFDOs) are Federal law enforcement officers commissioned by the Department of Homeland Security. FFDOs act under the umbrella of Transportation Security Administration Office of Law Enforcement branch - the Federal Air Marshal Service. The Federal Flight Deck Officer program is run by the Federal Air Marshal Service with the aim of training active and licensed airline pilots to carry weapons and defend commercial aircraft against criminal activity and terrorism. Upon completion of government training selected pilots enter a covert law enforcement and counter-terrorism service. Their jurisdiction is normally limited to a flight"
"for example, ""d"" is, specifically, an abbreviation of the verb ""do;"" the noun ""do"" representing the note of the musical scale is a different word, and must be spelled out. Portions of words may be contracted, and many rules govern this process. For example, the character with dots 2-3-5 (the letter ""f"" lowered in the Braille cell) stands for ""ff"" when used in the middle of a word. At the beginning of a word, this same character stands for the word ""to""; the character is written in braille with no space following it. (This contraction was removed in the Unified"
"(or (0,1) -tensor) on ""W"", so that ""F"" is an element of ""W"", the dual space of ""W"", then Φ""F"" is an element of ""V"", and so pullback by Φ defines a linear map between dual spaces which acts in the opposite direction to the linear map Φ itself: From a tensorial point of view, it is natural to try to extend the notion of pullback to tensors of arbitrary rank, i.e., to multilinear maps on ""W"" taking values in a tensor product formula_5 of ""r"" copies of ""W"". However, elements of such a tensor product do not pull back"
"from propositional variables and other propositional formulas using propositional connectives. Examples of connectives include: The following are the connectives common to rhetoric, philosophy and mathematics together with their truth tables. The symbols used will vary from author to author and between fields of endeavor. In general the abbreviations ""T"" and ""F"" stand for the evaluations TRUTH and FALSITY applied to the variables in the propositional formula (e.g. the assertion: ""That cow is blue"" will have the truth-value ""T"" for Truth or ""F"" for Falsity, as the case may be.). The connectives go by a number of different word-usages, e.g. ""a"
"character to a unique number. The COMMENT command (abbreviation C) creates a remark. The DO command (abbreviation D) branches execution to a subroutine; the subroutine is referenced either by group number or line number. Execution is resumed at the next statement once a RETURN is encountered. The FOR command (abbreviation F) provides for a loop. When three arguments are specified, the first is the initial value of the loop variable; the second is the increment (assumed to be 1, if omitted), and the third value is the terminating value for the loop. A sample FOR loop: The GO command (abbreviation"
"these characters represent companies, platoons and sections respectively, so that 3 Section, 1 Platoon of F Company might be F13. In addition, a suffix following the initial call sign can denote a specific individual or grouping within the designated call sign, so F13C would be the Charlie fire team. Unused suffixes can be used for other call signs that do not fall into the standard call sign matrix, for example the unused 33A call sign is used to refer to the company sergeant major. No call signs are issued to transmitters of long-range navigation systems (Decca, Alpha, Omega), or transmitters"
"SOE F Section networks These are the networks, also known as circuits, (or réseaux to their French participants) established in France by F Section of the British Special Operations Executive during the Second World War. This group(s) were tasked with the assignment of gathering information about the enemy and relaying said information to the SOE headquarters in London. At minimum, a circuit would be composed of three people: 1) Circuit leader: organize the group and recruit new members. 2) Wireless Radio Operator: know-how to work the wireless set, possessed an understanding of Morse Code and as well the ability to"
"""F"" is an object ""N"" of ""C"" together with a family ψ : ""N"" → ""F""(""X"") of morphisms indexed by the objects ""X"" of ""J"", such that for every morphism ""f"" : ""X"" → ""Y"" in ""J"", we have ""F""(""f"") ∘ ψ = ψ. A limit of the diagram ""F"" : ""J"" → ""C"" is a cone (""L"", φ) to ""F"" such that for any other cone (""N"", ψ) to ""F"" there exists a ""unique"" morphism ""u"" : ""N"" → ""L"" such that φ o ""u"" = ψ for all ""X"" in ""J"". One says that the cone (""N"", ψ)"
"as the Fightin’ Crawdads in reference to the crawfish featured prominently in the FST logo. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA527615 Fleet Survey Team Composed of approximately 65 military and civilian members, Fleet Survey Team (FST) is collocated with the Naval Oceanographic Office and Commander, Naval Meteorology and Oceanography Command, at Stennis Space Center, MS. FST, an echelon-five command since 2006, is tasked with performing an unparalleled function within the U.S. Navy. The command enables combatant commanders with access in the littoral regions through expeditionary hydrography. When forces are armed with detailed descriptions of the environmental conditions they could face, operations have a greater chance"
"with friendly aircraft and accidental mid-air bomb strikes. Dorsal gunner A dorsal gunner, mid-upper gunner or top gunner is an air gunner responsible for operating a gun position or turret located on the upper (dorsal) fuselage, between the cockpit and tail of some military aircraft. Between World War I and the 1950s, most heavy bombers, large attack/strike aircraft and long-range maritime patrol aircraft featured a dorsal, mid-upper or top gun position. During World War II, the mid-upper gunners of British Commonwealth heavy bomber crews were regarded as the primary observer of a crew, and were responsible for detecting the approach"
"flow (i.e they are mutually perpendicular) . A left hand can be held, as shown in the illustration, so as to represent three mutually orthogonal axes on the thumb, fore finger and middle finger. Each finger is then assigned to a quantity (mechanical force, magnetic field and electric current). The right and left hand are used for generators and motors respectively. Van de Graaff's translation of Fleming's rules is the FBI rule, easily remembered because these are the initials of the Federal Bureau of Investigation. This uses the conventional symbolic parameters of F (for Lorentz force), B (for magnetic flux"
"acting on a Hilbert space ""H"", and Ω is a separating and cyclic vector of ""H"" of norm 1. (Cyclic means that ""MΩ"" is dense in ""H"", and separating means that the map from ""M"" to ""MΩ"" is injective.) We write formula_1 for the state formula_2 of ""M"", so that ""H"" is constructed from formula_1 using the GNS construction. We can define an unbounded antilinear operator ""S"" on ""H"" with domain ""MΩ"" by setting formula_4 for all ""m"" in ""M"", and similarly we can define an unbounded antilinear operator ""F"" on ""H"" with domain ""M'Ω"" by setting formula_5 for ""m"""
"(FIR). This airspace is split into five ""Local Area Groups"" (LAGs) which relate to the position of the airspace sector groups within the FIR. All sectors have the R/T callsign ""London Control"". Also within the AC Operations room sit the FIR Flight Information Service Officers (FISOs) who provide an information service to aircraft operating within the London FIR as a whole using the callsign ""London Information"". 'Swanwick Military' controllers are also based in the AC Operations room. Each sector is assigned a sector number which is used when co-ordinating the passage of aircraft between each other. Colloquial names are also"
"Concerned Foreign Service Officers Concerned Foreign Service Officers (CFSO) is a group of current and former Foreign Service and Civil Service employees of the U.S. Department of State, cofounded by William Savich and Daniel M. Hirsch, created to investigate, document and expose alleged misuse of the security clearance process by the State Department's Diplomatic Security Service (DSS). CFSO's concern is the possibility that the clearance process can be used to circumvent Federal personnel regulations, to bypass equal employment opportunity laws and to punish dissenters and whistle blowers within the agency. The group investigates and documents allegations of improper and coercive"
"the diffeomorphism group of the circle with coefficients in the module of densities of degree 2 on the circle. Let ""F""(S) be the space of tensor densities of degree λ on S. The group of orientation-preserving diffeomorphisms of S, Diff(S), acts on ""F""(S) via pushforwards. If ""f"" is an element of Diff(S) then consider the mapping In the language of group cohomology the chain-like rule above says that this mapping is a 1-cocycle on Diff(S) with coefficients in ""F""(S). In fact and the 1-cocycle generating the cohomology is ""f"" → ""S""(""f""). The computation of 1-cohomology is a particular case of"